JEE Main Mathematics — Algebra previous year questions with solutions.
The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word 'SYLLABUS' such that two letters are distinct and two letters are alike, is
If $a,b$ and $c$ are the greatest values of ${C}_{p}19,{C}_{q}20$ and ${C}_{r}21$ respectively, then:
Let $a,b\in R,a\neq 0$ be such that the equation, $a{x}^{2}-2bx+5=0$ has a repeated root $\alpha ,$ which is also a root of the equation, ${x}^{2}-2bx-10=0.$ If $\beta$ is the other root of this equation, then ${\alpha }^{2}+{\beta }^{2}$ is equal to:
Let $a,b,c\in R$ be all non-zero and satisfies ${a}^{3}+{b}^{3}+{c}^{3}=2$. If the matrix $A=[\begin{matrix}a & b & c \\ b & c & a \\ c & a & b\end{matrix}]\begin{matrix} \\ \\ \end{matrix}$ satisfies ${A}^{T}A=I,$ then a value of $abc$ can be
For which of the following ordered pairs $(\mu ,\delta ),$ the system of linear equations $x+2y+3z=1$ $3x+4y+5z=\mu$ $4x+4y+4z=\delta$ is inconsistent?
Let $A=[\begin{matrix}x & 1 \\ 1 & 0\end{matrix}],x\epsilon R$ and ${A}^{4}=[{a}_{ij}].$ If ${a}_{11}=109,$ then ${a}_{22}$ is equal to_____________.
If the sum of the series $20+19\frac{3}{5}+19\frac{1}{5}+18\frac{4}{5}+..........$ up to ${n}^{\text{th }}$ term is $488$and the ${n}^{\text{th }}$ term is negative, then :
Set $A$ has $m$elements and set $B$ has $n$elements. If the total number of subsets of $A$ is $112$ more than the total number of subsets of $B$, then the value of $m\cdot n$ is___.
If ${p}$ denotes the fractional part of the number $p,$ then ${\frac{{3}^{200}}{8}}$ is equal to
If ${z}_{1},{z}_{2}$ are complex numbers such that $Re({z}_{1})=|{z}_{1}-1|$ and $Re({z}_{2})=|{z}_{2}-1|$ and $\mathrm{arg}({z}_{1}-{z}_{2})=\frac{\pi }{6}$, then $Im({z}_{1}+{z}_{2})$ is equal to :
If $z$ is a complex number satisfying $|Re(z)|+|Im(z)|=4,$ then $|z|$ cannot be
A survey shows that $73%$ of the persons working in an office like coffee, whereas $65%$ like tea. If $x$ denotes the percentage of them, who like both coffee and tea, then $x$ cannot be:
If$A=[\begin{matrix}\mathrm{cos}\theta & \text{ isin}\theta \\ \text{isin}\theta & \mathrm{cos}\theta \end{matrix}],(\theta =\frac{\pi }{24})$ and ${A}^{5}=[\begin{matrix}a & b \\ c & d\end{matrix}],$ where $i=\sqrt{-1}$, then which one of the following is not true?
If $A=(\begin{matrix}2 & 2 \\ 9 & 4\end{matrix})$ and $I=(\begin{matrix}1 & 0 \\ 0 & 1\end{matrix}),$ then $10 {A}^{-1}$, is equal to.
Let $S$ be the set of all integer solutions $(x,y,z)$ of the system of equations $x-2y+5z=0$ $-2x+4y+z=0$ $-7x+14y+9z=0$ such that $15\leq {x}^{2}+{y}^{2}+{z}^{2}\leq 150$. Then, the number of elements in the set $S$ is equal to ..........
The value of${(\frac{-1+i\sqrt{3}}{1-i})}^{30}$ is :
If the system of linear equations $x+y+3z=0$ $x+3y+{k}^{2}z=0$ $3x+y+3z=0$ has a non-zero solution $(x,y,z)$ for some $k\in R,$ then $x+(\frac{y}{z})$ is equal to :
For a suitably chosen real constant $a$, let a function, $f:R-{-a}\rightarrow R$ be defined by $f(x)=\frac{a-x}{a+x}$. Further supposed that for any real number $x\neq -a,$and $f(x)\neq -a,(\mathrm{fof})(x)=x$. Then $f(-\frac{1}{2})$ is equal to :
Suppose that a function $f:R\rightarrow R$ satisfies $f(x+y)=f(x)f(y)$ for all $x,y\epsilon R$ and $f(1)=3$. If $\sum _{i=1}^{n}f(i)=363$, then $n$ is equal to ..... .
The minimum value of ${2}^{\mathrm{sin}x}+{2}^{\mathrm{cos}x}$ is :
Let $f:R\rightarrow R$ be a function which satisfies $f(x+y)=f(x)+f(y),\forall x,y\in R$ . If $f(1)=2$ and $g(n)=\sum _{k=1}^{(n-1)}f(k),$$n\in N$ then the value of $n$, for which $g(n)=20$, is
Let $f:(1, 3)\rightarrow R$, be a function defined by $f(x)=\frac{x[x]}{1+{x}^{2}},$ where $[x]$, denotes the greatest integer $\leq x.$ Then the range of $f$, is
Let $\alpha$ be a root of the equation ${x}^{2}+x+1=0$ and the matrix $A=\frac{1}{\sqrt{3}}[\begin{matrix}1 & 1 & 1 \\ 1 & \alpha & {\alpha }^{2} \\ 1 & {\alpha }^{2} & {\alpha }^{4}\end{matrix}],$ then the matrix ${A}^{31}$ is equal to
If $x=\sum _{n=0}^{\infty }{(-1)}^{n}{\mathrm{tan}}^{2}\theta$ and $y=\sum _{n=0}^{\infty }{\mathrm{cos}}^{2n}\theta ,$ for $0<\theta <\frac{\pi }{4},$ then: